Optimal sensor and actuator locations in distributed parameter systems

The optimal sensor and actuator location problem in distributed parameter systems is considered. The sensor and actuator locations are chosen to minimize the performance criterion on the LQG problem with noises dependent on the actuator and sensor locations. The existence theorem for the optimal sensor and actuator locations is proved based on a property of evolution operators. Necessary and sufficient conditions are derived by using properties of operator-valued Riccati equations and evolution operators. It is shown that a duality holds between the sensor and actuator locations.